Re: (VU-Study-Corner) solution of MTH101 GDB (idea)

thank u so much

On Tue, Jul 5, 2011 at 10:20 PM, Muhammad Umair
<muhammad.umair.491@gmail.com> wrote:
> assalam o alaikum
> dear fellows, MTH101 ka GDB aaya hooa hai...
>  In the mean value theorems, we discuss the continuity of a given function
> in the closed interval and the differentiability in the open interval. Why
> we don't discuss its differentiability in the closed interval?
> yeh is liay k aik function [a,b] k closed interval par continuous tou ho
> sakta hai, par [a,b] par differentiable nahin ho sakta...
> example hai y = sqrt(1-x^2)
> yeh function x = -1 and 1 par continuous hai....par -1 aur 1 par
> differentiable nahin hai....
> yaad rakhain k mean value theorem mein hamain function k [a,b] k closed
> interval par differentiate honay ya nah honay se koi gharz nahin
> hoti....sirf [a,b] par continuous hona hi kafi hota hai...kyun k mean value
> theorem k mutabiq agar yeh teen cheezain satisfy hon
> 1. function is continuous on the closed interval [a,b].
> 2. function is differentiable on the open interval (a,b).
> tou [a,b] interval k darmiaan aik aisa point c hota hai jahan par
> instantaneous rate of change at that point, equal hota hai, overall average
> rate of change k, in the interval (a,b).
> average rate of change ka formula hai [ f(b)-f(a) ] / (b-a)...
> jab k point c choon k [a,b] interval k darmiaan lie karta hai aur function
> hamara continous hai tou point c par function differentiable bhi ho ga...
> is se yehi pata chalta hai k [a,b] par function k differentiable honay se
> hamain koi gharaz nahin hai....agar function end points par differentiable
> nah bhi ho tou tab bhi hamain koi faraq nahin paray ga aur ham mean value
> theorem apply kar sakain gay....
>
>
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